Research Article

Quantitative Susceptibility Mapping of Magnetic Quadrupole Moments

Figure 1

The dipole and quadrupole kernels in image- (top) and k-space (bottom). The kernels in image-space are based on (3) and (4), and those in k-space are based on (6) and (7). In image-space, all the kernels are real. The dipole kernel (d) decays as , and the quadrupole kernel () decays as . The dipole kernel, therefore, affects a wider range than the quadrupole kernel. In k-space, the dipole kernel (D) is real. The quadrupole kernel () is purely imaginary and proportional to . The magnitude of the quadrupole kernels, hence, increases as the k-coordinate increases.